1. Field of the Invention
The invention relates generally to progressive addition power ophthalmic lenses and, in particular, to an improved system and method for designing such lenses.
2. Description of the Related Art
Bifocal spectacle lenses have been used for many years by people suffering from presbyopia, a medical condition that causes loss of accommodation of the eye with advancing age resulting in difficulty focusing. Bifocal lenses provided a solution by dividing the lenses horizontally into two regions, each having a different optical power. The upper region of the lens was designed with the appropriate optical power for distance viewing, while the lower region was designed for closer viewing (e.g. reading). This allows the wearer to focus at different distances by merely changing their gaze position. However, wearers frequently experienced discomfort due to the abrupt transition between the different lens regions. As a consequence, progressive addition lenses were developed to provide a smooth transition in optical power between the regions of the lens.
Conventionally, progressive addition lenses are usually described as having three zones: an upper zone for far vision, a lower zone for near vision, and an intermediate progression corridor that bridges the first two zones. FIG. 1 is a diagram of a typical progressive lens shown in vertical elevation (plan view). The lens has a distance zone 2 with a given, relatively lower mean power and a reading zone 4 with relatively higher mean power. An intermediate progression corridor 6 of varying and usually increasing mean power connects the distance and reading zones. The outlying regions 8 adjoining the progression corridor and the lens boundary 10 (i.e. the edge of the lens) are also shown.
The goals in designing progressive lenses have been to provide both essentially clear vision in upper and lower zones 2 and 4 and smooth variation in optical power through the progression corridor 6, while at the same time to control the distribution of astigmatism and other optical aberrations.
Early design techniques required the lens to be spherical throughout the distance and reading zones, and employed various interpolative methods to determine the lens shape in the progression corridor and outlying regions. These techniques suffered from several disadvantages. Although the optical properties of the distance zone, reading zone, and progression corridor were usually satisfactory, regions adjoining the progression corridor and lens edge tended to have significant astigmatism. Interpolative methods designed to compress astigmatism into regions near the progression corridor yielded relatively steep gradients in mean power, astigmatism and prism. The resulting visual field was not as smooth and continuous as would be desirable for comfort, ease of focusing, and maximizing the effective usable area of the lens.
FIG. 2 shows a three dimensional representation of the mean power distribution over the surface of a typical progressive lens design. Mean power M is graphed in the vertical direction and the disc of the lens in shown against x and y coordinates. The disc of the lens is viewed from an angle less than 90° above the plane of the lens. The orientation of the lens is opposite of that in FIG. 1, the distance area with low mean power 12 shown in the foreground of FIG. 2 and the reading area with high mean power 14 shown at the back. Steep gradients in mean power are evident, especially in the outlying regions 16.
Many progressive lens design systems permit the designer to set optical properties at only a few isolated points, curves, or zones of the lens and employ a variety of interpolative methods to determine the shape and optical properties of the remainder of the lens.
U.S. Pat. No. 3,687,528 to Maitenaz, for example, describes a technique in which the designer specifies the shape and optical properties of a base curve running from the upper part of the lens to its lower part. The base curve, or “meridian line” is the intersection of the lens surface with the principal vertical meridian, a plane dividing the lens into two symmetrical halves. The designer is constrained by the requirement that astigmatism vanish everywhere along the meridian line (i.e. the meridian line must be “umbilical”). Maitenaz discloses several explicit formulas for extrapolating the shape of the lens horizontally from an umbilical meridian.
U.S. Pat. No. 4,315,673 to Guilino describes a method in which mean power is specified along an umbilical meridian and provides an explicit formula for extrapolating the shape of the remainder of the lens.
In a Jul. 20, 1982 essay, “The TRUVISION® Progressive Power Lens,” J. T. Winthrop describes a progressive lens design method in which the distance and reading zones are spherical. The design method described includes specifying mean power on the perimeters of the distance and reading zones, which are treated as the only boundaries.
U.S. Pat. No. 4,514,061 to Winthrop also describes a design system in which the distance and reading areas are spherical. The designer specifies mean power in the distance and reading areas, as well as along an umbilical meridian connecting the two areas. The shape of the remainder of the lens is determined by extrapolation along a set of level surfaces of a solution of the Laplace equation subject to boundary conditions at the distance and reading areas but not at the edge of the lens. The lens designer cannot specify lens height directly at the edge of the lens.
U.S. Pat. No. 4,861,153 to Winthrop also describes a system in which the designer specifies mean power along an umbilical meridian. Again, the shape of the remainder of the lens is determined by extrapolation along a set of level surfaces of a solution of the Laplace equation that intersect the umbilical meridian. No means is provided for the lens designer to specify lens height directly at the edge of the lens.
U.S. Pat. No. 4,606,622 to Furter and G. Furter, “Zeiss Gradal HS—The progressive addition lens with maximum wearing comfort”, Zeiss Information 97, 55–59, 1986, describe a method in which the lens designer specifies the mean power of the lens at a number of special points in the progression corridor. The full surface shape is then extrapolated using splines. The designer adjusts the mean power at the special points in order to improve the overall properties of the generated surface.
U.S. Pat. No. 5,886,766 to Kaga et al. describes a method in which the lens designer supplies only the “concept of the lens.” The design concept includes specifications such as the mean power in the distance zone, the addition power, and an overall approximate shape of the lens surface. Rather than being specified directly by the designer, the distribution of mean power over the remainder of the lens surface is subsequently calculated.
U.S. Pat. No. 4,838,675 to Barkan et al. describes a method for improving a progressive lens whose shape has already been roughly described by a base surface function. An improved progressive lens is calculated by selecting a function defined over some subregion of the lens, where the selected function is to be added to the base surface function. The selected function is chosen from a family of functions interrelated by one or a few parameters; and the optimal selection is made by extremizing the value of a predefined measure of merit.
In a system described by J. Loos, G. Greiner and H. P. Seidel, “A variational approach to progressive lens design”, Computer Aided Design 30, 595–602, 1998 and by M. Tazeroualti, “Designing a progressive lens”, in the book edited by P. J. Laurent et al., Curves and Surfaces in Geometric Design, A K Peters, 1994, pp. 467–474, the lens surface is defined by a linear combination of spline functions. The coefficients of the spline functions are calculated to minimize the cost function. This design system does not impose boundary conditions on the surface, and therefore lenses requiring a specific lens edge height profile cannot be designed using this method.
U.S. Pat. No. 6,302,540 to Katzman et al. discloses a lens design system that requires the designer to specify a curvature-dependent cost function. In the Katzman system, the disk of the lens is preferably partitioned into triangles. The system generates a lens surface shape that is a linear combination of independent “shape polynomials,” of which there are at least seven times as many as there are partitioning triangles (8:17–40). The surface shape generated approximately minimize a cost function that depends nonlinearly on the coefficients of the shape polynomials (10:21–50). Calculating the coefficients requires inverting repeatedly matrices of size equal to the number of coefficients. Since every shape polynomial contributes to the surface shape over every triangle, in general none of the matrices' elements vanishes. As a result, inverting the matrices and calculating the coefficients take time proportional to at least the second power of the number of shape polynomials.
The inherent inaccuracy of the shape polynomials (10:10–14) implies that the disk must be partitioned more finely wherever the mean power varies more rapidly. These considerations set a lower limit on the number of shape polynomial coefficients that would have to be calculated, and hence the time the system would need to calculate the lens surface shape. Since the Katzman system requires time that is at least quadratic in the number of triangles to calculate the lens surface, the system is inherently too slow to return a calculated lens surface to the designer quickly enough for the designer to work interactively with the system. The inherent processing delay prevents the designer from being able to create a lens design and then make adjustments to the design while observing the effects of the adjustments in real-time.
None of the above design systems provides a simple method by which the lens designer can specify the desired optical properties over the entire surface of the lens and derive a design consistent with those optical properties. As a consequence, many of these prior systems result in optical defects in the outlying regions of the lens and unnecessarily steep gradients in mean power. Furthermore, the computational complexity of some of the prior systems result in a lengthy design process that does not permit the lens designer to design the lens interactively. Many of the prior systems also do not include a definition of the lens height around the periphery of the lens and therefore do not maximize the useful area of the lens.